Here is how Mplus gets the LCA s.e.'s for the binary item parameters conditional on class in the probability scale.

After the ML solution in the usual logit scale has been obtained, the s.e.'s for the corresponding probabilities are computed using the Delta Method. This method draws on a Taylor expansion, boiling down to the following.

Note that with binary outcomes you get the probability from the logit by

(1) P = 1/(1+exp(-L)).

The variance, that is the squared s.e., is obtained by the Delta Method via the first-order derivatives as

(2) V(P) = dP/dL * V(L)* dP/dL,

where V(L) is the square of the s.e. for the regular Mplus estimates inlogit scale.

i have a question regarding the two-tailed p-value for the estimated probabilities conditional on class membership. does the program realize it is producing a p-value for a probability (which cannot be smaller than 0) and thus calculates a one-tailed p-value? if no, what do i have to do to get the one-tailed p-value? divide by two?